To make something heavenly or to transform something into a state resembling heaven.
From 'heaven' + '-ize' (suffix meaning 'to make' or 'to become'). The '-ize' suffix comes from Greek '-izein' and entered English through Latin and French. This verb formation is productive in English, allowing almost any noun to become a verb meaning 'to make into X.'
The '-ize' suffix is so powerful that English speakers can spontaneously understand new verbs instantly—if you 'sanitize' something, you make it sanitary, so to 'heavenize' something means to make it heavenly, even if you've never heard it before! This is called 'productive morphology' and it's one reason English is so flexible.
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